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Markus Hanke

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    2005
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Everything posted by Markus Hanke

  1. That’s because it is irrelevant, since the effect coming from metric expansion is many orders of magnitude greater than any net effect from gravity wells. Metric expansion does not happen within gravitationally bound systems on very small scales such as the distance Earth <> Sun. It’s not mentioned because the relative velocity between us and those bodies is small, so the amount of Doppler redshift is minuscule. It certainly does not contribute in any way to cosmological redshifts. The very first thing you have to do is actually understand current physics - you need to know exactly where we stand at the moment, both so far as large scale physics is concerned (GR, cosmology), as well as high-energy physics (quantum field theory, Standard Model). If you just reject the current paradigm without knowing exactly what it is you are arguing against, then no one is going to ever take you seriously. And herein lies the issue - the three biggest problems with what you are posting here are that 1. The idea of a massive photon is entirely incompatible with the Standard Model as we know it, and 2. You haven’t demonstrated that photons having rest mass is a concept that is actually able to replicate the phenomenology of dark matter, and 3. There are serious gaps in your understanding of current models You haven’t addressed point (1) at all, even though it has been pointed out to you. For point (2) you have offered only speculations that don’t even begin to address how massive photons are a viable explanation for dark matter. As for point (3), it’s kind of obvious that you really don’t know much about the basic models underlying current cosmology - for example your comment that, because light is deflected, it must have mass; or that mass is the source of spacetime curvature (both of these are inaccurate). So no, you don’t have to accept the Lambda-CDM model - but you are expected to thoroughly understand it in all its facets, before anyone will take you seriously. I see little evidence of that, to be honest (not intended as ad hominem, but simply a statement of fact based on your posts here). You also appear to forget that massive photons as explanation for dark matter is an old idea (“heavy light”), that has already been considered in detail by a number of physicists. But once you put some actual maths around this, it becomes obvious very quickly that it simply doesn’t work; even a photon with rest mass doesn’t have the right kind of properties to accurately account for the observed effects of dark matter. This general-reader type of article might be of interest: https://bigthink.com/starts-with-a-bang/heavy-light-dark-matter/ Hence, I maintain what I said earlier - interesting as a speculation, but a complete non-starter as a serious DM model.
  2. The mass can be small-ish, because it isn’t the mass itself the creates the destruction, but its kinetic energy from moving at high-relativistic speeds. The critical bit is getting the speed just right, because you wouldn’t want it to just punch through the target without expending its energy - the sun will be length-contracted into a flattened disk in the rest frame of the projectile. Exactly.
  3. No. The issue is, rather, that the concept of photons having rest mass is a pretty old idea, and has already been extensively tested in numerous high-precision experiments. Here’s the current status for both mass and charge for photons: https://pdg.lbl.gov/2020/listings/rpp2020-list-photon.pdf As you can see, the currently applicable upper bound is on the order of \(m<10^{-26}eV\), which is way too small by many orders of magnitude to account for the observed dark matter effects. It has also been pointed out already that a massive photon would have other consequences within the Standard Model, none of which we observe in the real world. Thus, as things stand at the moment, the idea is a non-starter from the beginning.
  4. No it is not. As has already been explained multiple times now, the two observers do not use the same notion of time when they are discussing in-fall time in their respective frames - hence you are not comparing the same quantities, and thus there can’t be a contradiction. Let’s be explicit here, so we can put this baby to bed once and for all. Suppose we have a particle in Schwarzschild spacetime starting out at rest at some initial radial position \(r_0\), which we can take to be far from the black hole, so that it initially corresponds to a far-away stationary Schwarzschild observer. It is then released and begins a radial free fall towards the horizon at \(r_S\). For the Schwarzschild observer (stationary and far away), the time it takes for the particle to reach the horizon, as measured on his own clock is (in natural units): \[\Delta t=\int _{r_{0}}^{r_{S}}\left(\frac{dt}{dr}\right) dr=-\int _{r_{0}}^{r_{S}}\frac{1}{\sqrt{2\left( 1+\frac{M}{r}\right)\left( 1-\frac{r_{s}}{r}\right)}} dr\ \rightarrow \infty\] This is coordinate in-fall time, since we’re integrating the ratio dt/dr, the expression for which follows from the equation of radial motion. On the other hand, the in-fall time as measured on the falling particle’s own clock is \[\Delta \tau =\int _{r_{0}}^{r_{S}}\left(\frac{d\tau }{dr}\right) dr=\frac{1}{3}\sqrt{\frac{2}{M}}\left(\sqrt[3]{r_{0}} -\sqrt[3]{r_{S}}\right)\] which is the proper in-fall time, and it is very much finite, as you can hopefully see. This expression comes straight from the metric. In order for there to be a contradiction, it would have to be the case that the length of the world line of the in-falling particle takes on different values for different observers; however, this is not the case, since \(\Delta \tau\) is a rank-0 tensor, so it is generally covariant, and thus all observers agree on it. To sum up: \(\Delta \tau\) is the length of the in-falling particle’s world line in spacetime, and the same for all observers \(\Delta t\) is not in general the length of the in-falling particle’s world line in spacetime, and explicitly depends on which observer is chosen These just simply aren’t the same physical quantities. Thus \(\Delta \tau \neq \Delta t\) isn’t a contradiction, but a necessary consequence of being in a curved spacetime, since time here is a local quantity. You can’t compare apples and oranges, and then claim there’s a contradiction because they don’t look the same. You have to compare apples to apples instead: In the frame of the falling particle, the length of its in-fall world line in spacetime is \(\Delta \tau\). In the frame of the distant stationary observer, the length of the particle’s in-fall world line in spacetime is also \(\Delta \tau\). It’s precisely that world line and its geometric length that your God-observer would see. No contradictions to be found anywhere - quite the contrary actually, since both observers are in perfect agreement about the length of that world line! PS. Why is it then that the far-away stationary observer never visually sees the particle reach the horizon? That’s because in-fall geodesics aren’t the same as outgoing geodesics. A photon originating close to the horizon can only escape to infinity via a trajectory that’s “flattened” tangentially to the horizon; the relative angles as seen by Schwarzschild and shell observers are related via \[\tan \theta _{shell} =\sqrt{1-\frac{2M}{r}}\tan \theta _{Schw}\] The closer to the horizon one gets, the more tangential the escape trajectories become, and at the photon sphere the angle is so small that nearly all photons become trapped into unstable orbits. Below this point, from the horizon down, the photon must fall in. This is why the Schwarzschild observer never visually sees anything reaching the horizon - because the closer one gets to the horizon, the fewer photons manage to escape back out to reach that observer, resulting a “dimming” of the object as seen by the outside observer (they are also red-shifted, resulting in further dimming). Once the photon sphere is reached, nearly all emitted photons are either captured into orbits, or must fall in, so the object becomes essentially invisible to outside observers. Only under very special circumstances can individual photons escape from here. Once the horizon itself is reached, no escape is possible at all, not even for photons, because null geodesics are everywhere perpendicular to the radial direction (the horizon is a null surface). Due to the symmetries of Schwarzschild spacetime, the coordinate time of a distant observer is defined such that it reflects precisely this difference between ingoing and outgoing null geodesics - it diverges to infinity precisely because no photon can ever reach this observer from the horizon, so nothing is ever visually seen to be reaching that point. This is in contrast to ingoing geodesics, which can be perfectly radial everywhere. Thus there is no contradiction, because ingoing and outgoing null-geodesics simply aren’t the same, not even in this highly symmetric spacetime.
  5. Just aim at the central star then, instead of the individual targets. It will take a larger mass and higher speeds, but it’s still doable.
  6. I suspect this is in reference to the BH thread you had started, and the supposed contradiction due to different observers disagreeing on in-fall times. I remind you once again that the two reference frames in question do not deal with the same premise, because they do not share the same notion of ‘time’. To cast it into the terms used here, the P belonging to the frame of the in-falling particle is not the P belonging to the frame of the distant stationary observer - you are comparing proper and coordinates times, but those are very different things. To make a valid comparison, you need to choose a physical premise that does not depend on your choice of observer - in this case the obvious choice is the length of the in-falling particle’s world line, ie proper in-fall time. For the in-falling observer, this world line is of finite length; for the distant stationary observer, this same world line is also of finite length. They both agree that the particle reaches the horizon, if you use the correct premise. The only difference is that the distant observer never sees this happening (which should be obvious, pardon the pun), whereas the infalling observer does. This is why it is important to grasp the very crucial difference between ‘global’ and ‘local’.
  7. Yes, that was precisely the problem I was getting at.
  8. Unfortunately I have yet to find good literature on this topic that is accessible to the general reader. Most papers about this spacetime out there are quite mathematical, including the one you quoted. If I can find anything, I’ll post it here on the forum. Generally speaking, the Vaidya solution is a generalisation of Schwarzschild in that spacetime isn’t assumed to be empty, so it is one of the simplest non-vacuum solutions to the field equations. It’s basically the kind of geometry you get for a spherically symmetric, non-charged, non-rotating body immersed in uniformly ingoing or outgoing matter or radiation. As a result, the parameter M in the metric now depends explicitly on time, so this is can be used as a toy model for a growing or evaporating black hole.
  9. Well, it would be like being confined to a perfect sensory deprivation chamber that is somehow able to completely suppress all external inputs. All that remains than are internal inputs, ie thoughts, memories, dreams, etc etc. Most people will probably consider this the highest form of torture. I can’t really answer these questions, also because this is not my area of expertise. Out of all the current attempts to explain consciousness, Integrated Information Theory seems to make the most sense to me, in which case the precise nature of the physical substrate underlying consciousness really isn’t relevant. Neurons are an extremely efficient solution, but in principle at least a network of machines that work in similar ways should do the job just as well. And yes, if IIT holds any water at all, then there should be degrees of consciousness, depending on complexity and structure of the network in question. In the future there might be ways to experimentally test this, but right now I think it’s pretty much all conjecture.
  10. Precisely! +1 No such observers physically exist. The closest you can come to it is to describe the situation only in terms of generally covariant quantities, ie quantities that do not depend on the choice of observer at all - meaning all physical observers must necessarily agree on them. That’s pretty much a God’s eye view on the situation. Mathematically, this means tensors (and spinors) of any rank will be used to describe the physics. For the situation at hand, the obvious choice would be the length of the in-falling particle’s world line (which is by definition equal to proper in-fall time) - which is finite and well defined, and as being a rank-0 tensor everyone agrees that it is finite and well defined. There’s also another issue - coordinate in-fall time diverging to infinity is valid only in Schwarzschild spacetime, which relies on a number of boundary conditions, most notably asymptotic flatness. In other words, to get Schwarzschild spacetime, you need to assume that the universe is everywhere completely empty so that spacetime far from the black hole is approximately flat. Obviously, in the real world, this only ever holds at most as a rough approximation - in reality, there will be stuff orbiting or falling into the black hole, and other gravitational sources at various distances. If you account for in-falling matter and/or radiation, but retain all other symmetries, then you end up with a different kind of spacetime, called Vaidya spacetime - and here even the coordinate in-fall time as measured by a distant observer is quite finite (though much longer than the proper in-fall time in the particle’s frame).
  11. No, not really. I was just aiming at the question of how to define “conscious”, as opposed to a machine that merely appears to be conscious. The difference between these is surprisingly hard to define. As for the nature of consciousness itself, I would conjecture that it probably arises as a global property of a complex system such as the brain, so I would think it resides in the global connectome and signal timings of the brain, rather than the nature of the individual building blocks. So if you were to replace all the neurons with machines that process inputs and outputs in the same manner, and are connected in the same way, then that new machine brain should be just as conscious. But of course, that’s purely conjecture - perhaps I’m entirely wrong on this. Yes, I did mention that we need to provide sensory channels, or else the results will be unpredictable. It would also be an ethical issue - imagine finding yourself conscious as a disembodied brain with all sensory channels turned off? Not good.
  12. Yes, but evolution continues to function, meaning those chimps will continue to evolve - what will they look like in another million years?
  13. All very good points +1 Just in case it came across differently - I am not trying to be argumentative about any of this. The reality of the situation is that we are all speculating here; there is really no hard data available to us to privilege any of the possible solutions to the Fermi paradox over any other, never even mind the issue of us not even knowing the complete set of all possible solutions. I simply think that DF is a scenario that, based on what we do know, and based on certain mathematically considerations, cannot be readily dismissed - as unsatisfying and scary as it is. But truth be told, this is one issue where I would genuine love to be proven entirely wrong
  14. There are no searches for the graviton taking place, for two fundamental reasons: 1. There is simply no physically reasonable detector that would be able to unambiguously detect individual gravitons, since their interaction cross section is so extremely small 2. The concept of ‘graviton’ comes from applying the tools of quantum field theory to General Relativity, in the same way as we do for the other forces. We already know that the resulting model cannot be renormalised - it contains infinities that cannot be removed, and thus it is impossible to extract physically meaningful predictions from such a theory. Gravity just doesn’t work the same way as the other interactions. It is therefore highly doubtful that the naive concept of ‘gravitons’ has any physical meaning at all.
  15. But that doesn’t answer the original question. How do you define “conscious”? It seems to me that there’s really no objective standard for this; it relies entirely on either self-reporting, or on behavioural analysis, neither of which are reliable indicators. Or let me put the question differently - suppose you build a machine the goal of which is to approach the anatomy and function of the human brain as closely as possible. The basic building blocks are miniaturised computers that process inputs and produce outputs in the same way as neurons do, ie as electrochemical potentials with the proper timing. You start with a single one of these - I think we can all agree that there’s no conscious experience here yet. Now you begin to add more and more of these computers, and connect them together at the same degree of network complexity as would be found with real-life neurons in the human brain. Further assume that along the way you provide sensory channels similar to those us humans have, but all based on miniature computers. Will this network ever become conscious? At what point does this network become “conscious”? And how can you tell that it has become conscious? Remember we will eventually have an exact replica of the human brain, except that, instead of biological neurons, it is made of computers.
  16. Yes, that’s a good point. I should remind you though that the concept I described about relativistic projectiles was just my own idea of the simplest possible way to go about this. Obviously, if the target civilisation is spread out, then this would call for more sophisticated tactics. No, it’s just game theory. I kind of come from the opposite direction - I find the assumption that all advanced civilisations must necessarily be ethical and/or benevolent to be questionable. It is also a very dangerous assumption, should you get it wrong. Of course I would want the more benevolent scenario to be the case, but…well. I’m personally hoping you are right. Unfortunately, Bright Forest (which btw isn’t an official term, it’s just something I came up with in my last post) relies on these civilisations either being able to effectively communicate and thus come to an agreement that ensures peaceful coexistence; or on there being some kind of universal ethics that is somehow shared between all highly developed forms of life, even prior to contact, and which prevents someone acting like in the DF scenario. Effective communication is highly constrained by the laws of physics, as described in my last post, and also by the compatibility problem. Basically, if you aren’t reasonably close to one another, both in spatial as well as psycho-cultural terms, then meaningful communication will be extremely difficult. I find it exceedingly unlikely for this not to be the case, unless the galaxy is swarming with intelligent species in close proximity who have somehow all managed to work around the compatibility problem. As for ethics, there’s really nothing at all we can say, since we ourselves are the only available data point. So I can’t guess as to any probabilities here. It’s too late for this anyway. We’ve been unwittingly bleeding all manner of obviously artificial EM radiation out into the cosmos, so if there’s anyone within a radius of ~100LY or so who cares to monitor these EM bands using sensitive enough receivers, then they will already know that we are here. For better or worse, the stay silent option is no longer available to us.
  17. It causes a clash only so long as you tacitly assume that there is only one concept of ‘time’ that is somehow equally valid for every observer anywhere in the universe. But GR tells us that this is not so - there is no global, universal time. There are only local clocks, meaning time is a purely local concept. And because time is local, you cannot use a distant, stationary clock to try and figure out what happens to an in-falling particle; you have to use a clock that is actually local (ie comoving) with that particle. That being said, it is important to remember that the distant stationary observer is still right about his own conclusions - but he is only right in his own frame of reference. For that distant observer, the particle really does never reach the horizon. Likewise, the observer attached to the in-falling particle is right about his conclusions, again in his own frame of reference; for him, the particle really does reach (and fall through) the horizon. So you have a situation where you got two observers who arrive at completely different conclusions, yet they are both right! This flies right in the face of everything we are used to, based on our own direct experience of what the world is like. But the trouble is that our experience is limited to a very specific domain - the classical, low-energy, low-velocity, non-relativistic, Euclidean domain. Within this domain, space and time have the same meaning everywhere, and can be neatly separated - so there is no distinction between “local” and “global” in that sense. But around a black hole, things are very different - time and space are inextricably intertwined, and measurements of time and distances are meaningful only within small local regions. You cannot project some specific observer’s notions of time and space someplace/sometime else, and expect to be able to tell what happens there locally. Needless to say, once the situation is analysed properly using the appropriate mathematical tools (which aren’t necessarily intuitive), there is no paradox, nor even a contradiction - this is all entirely self-consistent and logical, though counter-intuitive when viewed in light of our own Euclidean-based experience of the world.
  18. No, just the opposite - the entire scenario rests on the assumption that the laws of physics as we know them (specifically Special Relativity) cannot be circumvented, irrespective of your level of technological development. If it was possible to communicate FTL over large distances, then the parameters of the game will change fundamentally - you could then talk to the other races, observe them in real-time, ascertain their intentions, negotiate, and come to an agreement as to continued peaceful co-existence. Game theoretically, this will then become the most rational course of action. You could call this the “Bright Forest” scenario perhaps - it’s a situation where you can see the others, observe and study them, and find some way to coexist. The problem is that, given our current knowledge of physics, this scenario is ruled out on fundamental grounds. It’s not invasion, it’s annihilation. That’s not the same thing at all, because the latter is done from a distance. This is in fact disturbingly easy - all you need to do is fire a small, dense projectile (say for example a chunk of dense metal the size of an aircraft carrier) at just the right high-relativistic speed at the target planet. The speed must be just right - too slow and it won’t have the necessary oomph, too fast and it will likely punch right through the target and out the other side. But if it’s done right, all the kinetic energy should become free on impact. With catastrophic results. Of course this will still take time (and some accurate and reliable maths) to execute, given the distances involved, but it’s doable. All you need is enough energy, and some mechanism to sufficiently accelerate and aim your projectile, which shouldn’t be too difficult for an advanced civilisation. Yes. But game theoretically, in a scenario like DF, it is still the best and most rational among all realistically available options. What are the alternatives? You could just do your level best to ensure you remain invisible and undetectable to everyone else (hide); or you can simply not do anything and hope that the others won’t attack you due to ethical considerations (hope). Or you can take a gamble, and broadcast a message of the type “DON’T ATTACK WE ARE PEACEFUL” in all directions, and hope that anyone who picks it up will believe you. How credible such a message would be, given the state of current affairs here on Earth, is another question; and sending such a message would be like lighting a beacon, since everyone will know exactly where you are located. So it’s basically attack, hide, hope, or come out of hiding and show yourself. None of these are pretty, but it can be shown that pre-emptive attack will maximise your chances of survival in a game like this.
  19. I think you are using a different definition of ‘time’. In physics, not only can it pass, but it must do so by definition - time in this particular context is simply what clocks measure, and this is the definition I am using here. As such, everything always ages into the future, always and inevitably. That is precisely what “time passes” refers to in this context - the ageing of a physical system into the future, as measured by a comoving clock in its own reference frame. Thus, the body (as a physical system) is no longer in the same state when your subject awakens as it was when they fell unconscious. Time “passing” means that the co-moving clock has advanced. If you are using a different definition of time than physics does, then that’s fine (I know there are a few other possibilities), but you need to be explicit about which one it is you are using, because these concepts are not interchangeable. Of course. No one would claim such a thing. Your birthday is in the past, isn’t it? It hasn’t “moved through time” with you. The point though is that physical systems evolve (age) into the future irrespective of whether they are conscious or not, in the sense that a clock comoving with that system will inevitably advance. Yes, but this is useless for the purpose of doing physics, because there’s no physical instrument that can measure this in a repeatable and objective way. It isn’t even reliable for the observer himself, because the sense of subjective time is just a model constructed by the brain (as is the entirety of the “flow of experience”), and as such it can get distorted or fail in all manner of ways, eg through disturbances in brain chemistry, or as the result of particular types of brain injury (dyschronometria). The same is true for the sense of space, btw. I don’t know what this means, because physical time isn’t a ‘thing’ or a valid point of reference relative to which anything could flow; it’s just part of a map of events that we call ‘spacetime’. Are you claiming that consciousness is an ontological entity separate from spacetime and the particles/fields that live on it?
  20. Yes it does - he ages into the future regardless of whether he is aware of that or not. Even if the subject in question is the only observer, all he needs to do is measure the ratio of naturally occurring radioisotopes in his very own body before and after the period of unconsciousness, and it will be obvious to him that objective time has passed while he was ‘out’. The human body is essentially a giant clock in that sense, and this is an easy experiment to perform. Also, if he was out for long enough (eg in a long-term coma after serious head trauma), the fact will be rather obvious to him from the deterioration of muscle and bone when he reawakens, even without isotope measurements. From a physics point of view, all particles trace out world lines in spacetime, meaning they always age into the future, even if they remain static and stationary with respect to some reference point. PS. It is quite unwise to post your email address publicly on the Internet for anyone to read and any bot to harvest, unless you want your inbox to get inundated with spam.
  21. Yes, absolutely. That is why you need to remain invisible, undetectable, and silent yourself, so all anybody ever sees is at most shadows moving in the dark. If done right, your opponents won’t know where to direct that second shot at. It’s called ‘Dark Forest’ for precisely this reason - it’s a game of wiping out all potential threats, ideally before they even become aware of your own existence, in order to ensure your own survival. Like being lost in a deep dark forest, surrounded by silent and unseen predators. In this scenario, the resolution to the question of whether or not aliens exist might one day appear in the form of a small but massive projectile coming at us at high-relativistic speeds, and we’ll never even know who took the shot or where it came from. It’s pretty terrifying, and I sincerely hope this is not how things actually are out there. But unfortunately it is a rational scenario backed by game theory and fully compatible with the Fermi paradox, so one cannot simply dismiss it.
  22. You probably mean gravitational waves - gravity waves are a phenomenon in fluid dynamics, and have no relation to black holes. The answer to your question is threefold: 1. Gravitational radiation during BH mergers does not originate only at the event horizon, but results from the quadrupole moment of the binary system as a whole. Any kind of binary system - irrespective of what kind of objects it is comprised of - will be a source of such radiation. It is, in that sense, a global phenomenon of such spacetimes, and its source cannot be localised to any one particular point or region, including the event horizon. That being said, the geometry of the horizons reflect the geometry of all the rest of this spacetime (in very complex ways), so observing the wave forms of the radiation field allows you to extrapolate what happens at the horizon during the merger. This whole process is really a global one, and doesn’t just happen at the horizon. 2. The diverging in-fall time you are referring to applies to Schwarzschild black holes, but the spacetime in a binary system of in-spiralling BHs is not of the Schwarzschild type, not even approximately. Figuring out the precise in-fall time of a test particle from far away into one of these BHs is a highly non-trivial task, that can only be done numerically, but my guess is that it wouldn’t be infinite at all (one of the necessarily prerequisites for an infinite in-fall time is asymptotic flatness, which does not hold in this type of spacetime); it would also explicitly depend on where and when the test particle begins its free fall. 3. Even for Schwarzschild BHs, the infinite in-fall time applies only to test particles moving on time-like or null geodesics of the undisturbed background, ie it applies only to test particles whose own gravity can be neglected. This, however, is not the case for gravitational waves, which will couple to the background curvature in non-linear ways. To put it differently, a spacetime that contains gravitational radiation cannot have Schwarzschild geometry, and thus the infinite in-fall time does not necessarily follow. Even in cases where the gravitational waves are weak enough so that the background could still approximately be treated as Schwarzschild (which is not the case for a binary BH system!), the wave fronts wouldn’t propagate along the same trajectories as free-falling test particles, due to non-linear interactions with the background curvature. No it doesn’t. The length of the world line of a test particle free-falling from far away and crossing the horizon is finite and well defined; spacetime at and around the event horizon is smooth and regular, so time proceeds as normal there. The thing with this is that in curved spacetimes, there is an important difference between coordinate in-fall time and proper in-fall time. The coordinate in-fall time is what a distant observer will calculate and observe, based on his own instruments, which are not themselves located at the horizon; the numerical value of this will depend on which observer you choose. The proper in-fall time, on the other hand, is what is directly measured by a clock that is attached to the freely falling test particle itself; by definition, it equals the length of that particle’s world line through spacetime. For the case of a test particle freely falling into a Schwarzschild black hole, a far-away stationary observer will determine a coordinate in-fall time that diverges (goes to infinity). However, the proper in-fall time of that same test particle is finite and well defined, so the particle reaches the horizon in a finite amount of time as measured by its own clock, and continues falling through the horizon and into the singularity (also in a finite, well defined amount of time). Because of the way that proper time is defined mathematically, all observers agree on it. On the other hand though, coordinate time is always specific to a chosen observer, and not valid anywhere else. In curved spacetimes, time is a purely local phenomenon; a far-away observer does not share any concept of simultaneity with processes that happen at the (for him) distant horizon.
  23. Yes, that’s a good and valid point. However, one must remember that we ourselves don’t hesitate to annihilate large groups of sentient individuals belonging to other species, if our own interests are threatened. Consider - just as a random example - spraying large swathes of agricultural land with insecticides, which is still common practice in many places. Such acts lead to the death of millions of insects, and we don’t bat an eyelid. Why? Because very many people do not consider insects to be worthy objects of moral concern, since we regard them as primitive, expendable, undeveloped, unintelligent, and a direct threat to our own interests. If they annoy or threaten us, we simply annihilate them. The crucial factor in the DF scenario is incompleteness of information. If two civilisations are, say, 10000LY apart (not unreasonable if there are only a handful per galaxy), and assuming the laws of relativity as we know them cannot be circumvented in some way, then there simply isn’t any workable method for these civilisations to talk to each other in any meaningful sense. As a consequence, neither one of them can truly know what the intentions of the other one are, and (more importantly) what their current level of development and technology capability is, since the latest available information about them will be 10000 years old. You cannot extrapolate how a civilisation might develop over such long periods of time, especially not based on limited data. So you are pretty much left completely in the dark - you have no way of knowing what they are up to, what their intentions are, and how they think about you. Of course you can assume that they are moral beings, but that’s a huge gamble to take, and if you’re wrong then that’s the last mistake you’ll ever make. So that’s the basic conundrum - the speed of light is very slow when taken to even just galactic scales.
  24. True. And personally I’m partial to the third option - that we simply aren’t going to see any alien civilisations any time soon. But we may well see more primitive forms of extraterrestrial life in the near future, perhaps even within our own solar system. I’d also like to point out that, in a Dark Forest scenario, a civilisation acting in the most rational way within the confines of that mathematical game (ie eliminating other civilisations) does not imply malevolence on their part. They simply do what they need to in order to maximise their own evolutionary potential in what is a scenario with few other options, given the constraints imposed by the laws of physics. Even an otherwise benevolent and ethical civilisation may find it necessary to take such drastic steps. Also, just because we place a high ethical value on life (do we??) does not necessarily mean that others share this concept.
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